It is not at all clear that it is easier to improve by a fixed percentage on harder problems than it is on easier ones. Back in the days of the Bain Experiment, I found that reducing my solution times by a fixed percentage for my first pass through the first batch of problems gave a good fit to my solution times on the first passes through the later batches of problems. That appears to be roughly right for Woolum too.
I advocate to train every specific task that you have to perform in a specialized way. Optimized for that specific task. Preventing diminishing returns.
The first thing to do is to determine which tasks we are talking about. Every tasks has its own specialized sets of patterns associated with it, and if you don't find out which patterns to learn, chances are high that you don't learn these patterns at all.
First task: 20 tactical elements.
The first task we have identified is that we have 20 - 30 elementary tactical themes, depending on the source. Let's round it off to 20 usefull themes. In my opinion these are trained best according to my speedtraining method:
Make per tactical element a separate problemset with rating <1200. Solve these problems as fast as possible, untill you reach a speed of <4 seconds per problem. 1000x per tactical element is probably enough to recognize it everywhere and fast. Let's say a problem takes 20 seconds at average. This leads to a total time of 20 elements x 1000 times x 20 seconds = 111 hours to master this task.
Doing the same with combinations I consider to be useless, since there are way too much combinations.
Doing problems higher rated than 1200 is useless for this task. Here the law of diminishing results sets in soon.
Second task: guiding your mind for duplo attacks.
I identified duplo attacks as one of the three ways to gain wood. Traps and promotion being the other two. This means that you have to scan a position for all its duplo attacks. There are 5 different duplo attacks (double attack, discovered attack, pin, skewer, rontgen attack). The recognition itself of these 5 patterns is already taken care of when training for the first task. You only have to make it a habit to scan for all of these duplo attacks in stead of stopping short once you get distracted by one of them which looks promising.
I use high rated problems for this for a starter. Once I have identified all duplo attacks I store both the position and the duplo attacks as a flashcard in Anki and train them further with the aid of Anki, without going back to CT anymore.
Third task: making one of the duplo attacks work.
At average there are about 6 duplo attacks in a >2000 rated problem. Only one of them is winning. At this stage is is my task to find out which one and how I can make it work. For this I need all tactical elements that I have learned already in task one and that can act as some prelimanary move. Besides that, some conscious thinking is probably needed here in order to make it work.
Fourth task: identifying the focal squares.
The fourth task is needed to assist task three.
Once I know the target, I must find the way back to the attacker, finding the focal points along the road. These focal points give me clues to the preliminary moves I ave to make before the combination will work. I must identify the defenders of the focal points and find a way to annihilate them. I must identify where my own pieces get in the way and clear them, etc..
I use high rated problems for a starter. Once I have identified the focal points I make a flashcard with the position and the focal points. From there I train it with Anki.
Fifth task: learning the mating patterns.
This has great similarity with task one.
If I'm not mistaken there are 29 different mating patterns that must be learned. Speedtraining with <1200 rated problems will do the job.
Sixth task: learning the patterns that are associated with promotion.
This has great similarity with task one.
Speedtraining with <1200 rated problems will do the job.
Seventh task: Chasing the king.
I just discovered this as a problem. It has its own associated patterns. First I must formulate a search algorithm. In order to find one I use high rated problems at CT which are mates. Usually> 4 movers.
Only once I have found a suitable algorithm, I can start to think about a method how to train them.
To give you an idea of the complexity of the matter: a search algorithm must guide you through this testposition in order to be usefull.
Eight task: positional play.
Under construction. See previous posts.
Speed training with tagged low rated problems is suitable for most elementary patterns. High rated problems are used in two cases:
- As a starter to extract patterns that you will only find in complex problems. The actual learning is done with flashcards and Anki.
- During investigation. When you are investigating new tasks and defining new search algorithms. This is only temporarily.
It is true that you have an average of about 3 minutes per move in a standard time limit game, but how much time can you afford to spend on checking that your chosen move is proof against a tactical shot? I would have thought that 1 minute would be optimistic. Hoping for a sixty fold improvement in your solution time is too optimistic in my opinion.
That's all way too ridgid and too theoretical. We will find this out in an empyrical way.
What failure rate is acceptable when checking for tactical shots? 10%, 1% or less… There are typically about 40 moves in a game, and many or most of them could fall foul of tactical shots. If you accept a 10% failure rate, you are going to “blunder” once or more in most games. Even if you get your failure rate down to 1%, you will regularly lose to tactical shots.
Again way too theoretical. Not all positions call for an ability to solve tactics at 2300 level. But sometimes tactics just must work or you loose. If I look at the Polgar middlegame brick, I could flaw about 25% of the tactics that were presented there with the aid of Rybka. This means that both the grandmasters who played the game, the grandmasters that annotated the game in the Informator and Susan Polgar who checked the problems for the book overlooked the flaws. When both you and your opponent miss the same tactic, the tactic is irrelevant for the game.